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Off Topic => Test/Spam Forum => Topic started by: Simpsonboy77 on July 28, 2009, 08:48:39 PM

Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on July 28, 2009, 08:48:39 PM
A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?

Good luck
Title: A Women Has 2 Kids....
Post by: Sirbomber on July 28, 2009, 11:23:27 PM
A women?  How does that work?  Multiple personality disorder, or something?
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on July 29, 2009, 05:43:03 PM
Thats irrelevant.

There is a family with 2 children. One is a girl. What is the chance the other child is a girl?

Is that more clear?
Title: A Women Has 2 Kids....
Post by: WalkmanSilver on July 30, 2009, 04:54:05 AM
Well it depends who has the stronger genes I suppose
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on July 30, 2009, 06:06:05 PM
This isn't the point of the question :P.

Assuming the birth rate is 50:50, and for this  exercise assume the child cant be both or neither.
Title: A Women Has 2 Kids....
Post by: Hooman on July 30, 2009, 10:39:05 PM
Ok, 0.5, assuming they are independent events.
If you take world averages into account, it's more like 0.52 or something.

There are cases where it doesn't appear to be independent events, however, the sample size is too small to tell if that is the case. I assume the chance of some genetic condition favouring one of the other is quite small, and so probably won't have much of an effect on average. In some specific case, I suppose it might be large difference, but again, we don't have enough info to determine that and it would vary too much between cases to give any kind of answer here.


A typical wrong answer people give to independent event questions is 0.25, as they assume the first sample somehow has an effect on the second sample.
 
Title: A Women Has 2 Kids....
Post by: CK9 on August 01, 2009, 05:17:13 PM
I second hooman's response.  There are three main cases to consider: non-twin siblings, fraternal twins, and identical twins.  The first two have a 50% chance each, and the third has a 100% chance.  Therefore, 52% is the best assumption to go with.
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 02, 2009, 03:21:22 AM
Quote
Ok, 0.5, assuming they are independent events.
If you take world averages into account, it's more like 0.52 or something.

A typical wrong answer people give to independent event questions is 0.25, as they assume the first sample somehow has an effect on the second sample.
The first part you are correct, its not quite 50:50, but for the purposes of this lets just say it is.

Indeed many people give the wrong answer, and sorry to say you are one of them. Yes I am considering them separate events, so no twins or anything. I think I should have posed this question as flipping 2 coins instead.

All I say in the problem is one of them is a girl, so it could be the first or second. There are 4 possible combinations, BB BG GB GG. Now since one of them is a girl you can eliminate BB.

Now you are left with 3 groups with an equal chance of occurring, GG, GB, BG. Now only one of them has BOTH as girls, and out of 3 choices, so the correct answer is 33% (assuming birth rate is 50:50)

Don't worry only like .01% of people actually get this question correct on the first try. I got it wrong also hehe.
Title: A Women Has 2 Kids....
Post by: Hidiot on August 02, 2009, 05:18:44 AM
I call flaw on that judgment.

Since BG = GB.

No mention of which came first. That's important data for the problem, so I accuse you of giving a incomplete problem ( :P )
[size=8](I'm kidding about the accusing, of course)[/size]

And to add to that, there's a theory according to which, if the first child is a girl, chances for the second child to be a boy are less than 50%.
Title: A Women Has 2 Kids....
Post by: Hooman on August 02, 2009, 02:27:35 PM
My initial thought was there was a flaw in the argument, although, now I'm thinking the reason being that the information given implies something about both children. If you rephrase it, it's more like, given that at least one of the two kids is a girl, what is the probability that the second kid is a girl. You lose independence of events in this case. If the first is a boy, then you were talking about the second kid. If the second is a boy, then you were talking about the first kid. If they are both girls, then it doesn't matter which kid you were talking about.

When I first read it, I suppose I didn't quite read it carefully enough. I figured there was some trick to it that I wasn't quite seeing, which is mostly why I wrote that second part. Thought that might be the trick.

Of course, with the way the question is written, if "one" kid is a girl, then the probability of the other kid being a girl might very well be 0. :P
 
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 02, 2009, 08:05:48 PM
Yea I'm good at math but I fail at english (well not really its just significantly weaker).

Yes the given information takes both into account, it is not meant to be interpreted as ONLY the first or (more like XOR) the second.

I think the better way to phrase it would have been: "A women has 2 kids, and at least one of them is a girl. What is the chance that both children are girls?

EDIT: Forgot to address Hidiot's points

Hidiot BG is not equal to GB. They both are separate.  If you combine them then you must take into account the weighted chance since GG will occur half the amount of times of BG or GB. If you take all 3 as separate then they all have equal chances.

"And to add to that, there's a theory according to which, if the first child is a girl, chances for the second child to be a boy are less than 50%"
In the problem if you know the gender of the first then you can narrow it down quite easily. If it is B then the second kid must be G, otherwise its a 50:50. Or are you talking about real life, if so please elaborate I'm interested in this.
Title: A Women Has 2 Kids....
Post by: Hidiot on August 03, 2009, 02:07:58 AM
I was not very clear with BG=GB thing. It only happens when the order is not specified.


I'm talking about real life. I can't elaborate, it's something I heard about a few years back.
Title: A Women Has 2 Kids....
Post by: CK9 on August 03, 2009, 03:29:07 AM
simpson, I have to say that I'm shocked that I didn't think of it in that way.  Expecially since I did so well in the genetics portion of my bio class, it's the same basic thing as dmoinant and ressant traits with how you're looking at it

Quote
example
___|__B_|__b_
_B_|_BB_|_Bb_
_b_|_bB_|_bb_


however, for all intents and purposes, Bb is considered the same as bB, as both result in the same possible genetic exchanges.......

If you stated it with coins, though, I would have gotten it.  With children, you have too many additional factors that you have to consider when choosing your wording.
Title: A Women Has 2 Kids....
Post by: Eddy-B on August 03, 2009, 09:35:42 AM
Quote
A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?

I still say 50% chance (if assuming the ratio is 1:1 for boys:girls)

The first part can be totally ignored: it DOES NOT MATTER what sex the "one" child is, because the question is: what is the sex of THE OTHER ONE , which is still a 50-50 chance of being a girl.

No matter how you ask the question; the chance remains 50:50.
If you rephrase the question:
What is the chance the second born is a girl, when you know at least 1 of them is a girl?
The chance of any child being born a girl is still 50% and 50% for a boy - nothing changes that!


Next problem please :)
Title: A Women Has 2 Kids....
Post by: Freeza-CII on August 03, 2009, 12:49:33 PM
Its another hooman trick question

the real answer is hermaphrodite
Title: A Women Has 2 Kids....
Post by: Hooman on August 03, 2009, 02:47:31 PM
But Eddy, you're fogetting that they didn't specify which child. The selection of the kid for which information is given is done after both are born, and the sex is determined. If they first kid was a boy, then they must have been talking about the second. If the second kid was a boy, then they must have been talking about the first. Hence, the information given isn't actually for a single kid, but rather a merging of the info for both kids.


Remember conditional probability rule:
P(A|B) = P(A intersect B) / P(B)
The probability of A, given B, is the probability of A and B, divided by the probability of B.

The probability of A intersect B, that is, that both kids are girls, is 1/4. The probability of B, that at least one is a girl, is 3/4. Therefore the probability of both kids being girls, given that at least one kid is a girl is (1/4)/(3/4) = 1/3.

But yes, it would be more clear if it was worded, "What is the probability that both kids are girls, given that at least one kid is a girl".
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 03, 2009, 08:12:16 PM
I'm sorry for posting a trick question in a terrible form. Hooman's wording is best.

Your friend flips two coins, and does not tell you the outcome of each one. Instead he tells you that at least one of the 2 coins turned up heads. What is the chance that they are both heads?

Now for flipping coins you have 4 possibilities
HH
HT
TH
TT

We can eliminate TT since he said that at least one is heads. We are looking for BOTH to be heads which occurred 1 time, but there are only 3 valid outcomes. If you try this by your computer and you get TT, then consider that a reflip of BOTH.


Hooman has the math behind it, I didn't want to bore you with it yet.
Title: A Women Has 2 Kids....
Post by: Spikerocks101 on August 05, 2009, 01:35:37 PM
But you cant count HT and TH as 2 different things, since they are the same, because if I flip a coin right now, and it gets heads, I am pretty sure, that if I flip it 10,000 years form now on New Terra, it still has a 50% chance of getting heads, assuming the coin has no flaws what so ever. Its 50%, not 33%, or 25%. 33% is just making it confusing, but 25% is just wrong...

Edit: I agree with Hooman's refrasing of the question, for that makes sence...
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 05, 2009, 03:23:10 PM
How did this turn into a debate?  This shouldn't even be considered a trick question, unless you lack an understanding of basic genetics, which I shall now explain even though it's probably not necessary.

Basic genetics time (only looking at sex-determining genes, and assuming "normal" parents and children):
Father's genes: XY
Mother's genes: XX

XY + XX =
(http://i5.photobucket.com/albums/y197/Sirbomber/GeneticsStuff.png)

There's a 25% chance for any 4 of those possibilities being "chosen", but possibilities 1 and 3 are the same, as are 2 and 4.  For all intents and purposes there are 2 possibilities, each having a 50% chance of being "chosen".  And yes, "XY" and "YX" are the same thing, making Simpsonboy77's 33% argument wrong.  Poor wording does not make something a "trick" question; it just makes it stupid.

Edit: Forgot to mention: the global average is 52F:48M because men tend to die younger than women.
Title: A Women Has 2 Kids....
Post by: Hooman on August 05, 2009, 07:37:27 PM
Quote
Edit: Forgot to mention: the global average is 52F:48M because men tend to die younger than women.

Hmm, interesting point. I used to assume there was a difference in the birth rate rather than the death rate.


Still, there is a difference between BG/GB or HT/TH. You are not simply reflipping the same coin here and writing down the values in any order.

This problem is equivalent to having a 4 sided die, rolling it, telling someone that one of the sides that didn't come up (after rolling), and then asking them what the probability of any of the remaining sides comming up is. There are 3 equally likely outcomes left to choose from.


Edit: Btw, those genetic X/Y chromosone things are really irrelevant here. The problem is about two separate children. All you're stating with those charts is that the probability of a single child is 50:50, which we've already agreed upon.
 
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 05, 2009, 08:59:21 PM
Quote
How did this turn into a debate?  This shouldn't even be considered a trick question, unless you lack an understanding of basic genetics...
This wasn't even supposed to be a question of genetics, but a question of probability.

Agreed male to female birth ratios are close enough to be considered 50:50 (it is actually 106 males to 100 females) Living rates are flipped, as he stated above its 52:48.


Quote
There's a 25% chance for any 4 of those possibilities being "chosen"
Agreed.

Quote
but possibilities 1 and 3 are the same, as are 2 and 4. For all intents and purposes there are 2 possibilities, each having a 50% chance of being "chosen
Agreed.

Quote
And yes, "XY" and "YX" are the same thing, making Simpsonboy77's 33% argument wrong. Poor wording does not make something a "trick" question; it just makes it stupid.
I agree here as well, sort of. XY and YX are the same, but that is not what I was referring to. I was using BG and GB to show both children at once. The second you narrow it down to one child it instantly becomes 50%. This is because you added a restriction, you checked the second child knowing the outcome of the first.

We are talking about different levels in the problem. I never brought genetics into the equation. I took each possibility of occurring to be 50%, which you agree in point 2.

Now thinking that your table represents both children at the same time, it was made incorrectly. The Y axis should also be X and Y not X and X. I don't think this is the case since it is correct for a one child birth.


Let me try to break this down into the most atomic steps as possible. Tell me where you start to disagree with me.

1. Assume that birth rates are strictly 50% for each.
2. Assume a boy and boy birth cannot happen. This is stated in the question since at least one child is a girl.
I will branch right now in 2 paths.
3. First child is a boy so the second child MUST be a girl.
This is one possible outcome and it does not satisfy the desired outcome (GG). 0 out of 1 so far.
4. Assume a girl is born first.
5. Two outcomes are a girl birth and a boy second birth.
6. The second girl birth gives the desired scenario so we are 1 out of 2 right now.
7. The boy second birth is valid yet it is not what we want. So we are now 1 out of 3.

I have a feeling you are going to say that step 3 has a 50% chance of happening while 6 and 7 are both 25%. Remember once the first child is picked to be a boy there is still a 50% chance in that subset that the outcome is invalid. They all have equal possibilities, thus no weighted average is needed.


___|__B_|__G_
_B_|_BB_|_BG_
_G_|_GB_|_GG_
Here you can see there is a 25% chance of each happening, but BB is not possible due to the restrictions given. You are now down to 3 choices, but the chances do not change since they are "locked in".

When I said I worded it poorly, I was referring to just using people in general. I thought it would have sounded a bit more interesting than coin flips.
Title: A Women Has 2 Kids....
Post by: Eddy-B on August 06, 2009, 12:52:24 AM
Hooman:
i know what was the point of the "riddle" but the way the question is asked, the answer is still a simple 50:50  as it does not matter what sex the first one is, or even which child is the girl that was mentioned.
All that matters is the question at hand: WHAT IS THE CHANCE of the second baby to be a girl, which -simply put- is the global average of 48:52 or 50:50 as mentioned.

It's a simple given fact that the chance of ANY baby being born to be evenly split into boys or girls - and yes i had 2 years of mathematical chance calculus in highschool, as well as 6 years of biology (i was an A+ student at both) in which i learned about recessive & dominant genes and how to calculate those chances - but still : they don't apply to this question: the ORIGINAL question was (simplified) "what is the chance that the second baby is a girl" period.

 
Title: A Women Has 2 Kids....
Post by: CK9 on August 07, 2009, 03:32:59 AM
And that's why riddles have to be carefully worded, lol
Title: A Women Has 2 Kids....
Post by: Freeza-CII on August 07, 2009, 02:05:29 PM
that chances of the other one being a girl is 100% due to the fact of modern gene manipulation. you just got owned with science!
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 07, 2009, 11:45:55 PM
Quote
Hooman:
i know what was the point of the "riddle" but the way the question is asked, the answer is still a simple 50:50  as it does not matter what sex the first one is, or even which child is the girl that was mentioned.
All that matters is the question at hand: WHAT IS THE CHANCE of the second baby to be a girl, which -simply put- is the global average of 48:52 or 50:50 as mentioned.

Quote
A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?

I still disagree, poorly worded, yes, but it does tell you all the needed information.  It is not a 50% chance no matter how it is sliced, once again ignoring slight changes in birth rates. It asks for the chance of the second tested, not necessarily the second born, but it does include the needed clue, that one of them is a girl. If they are both girls, one of them is still a girl. If it said the first child is a girl, then yes it would be 50%, but it said one of them, which is referring to both children at once.

Quote
the ORIGINAL question was (simplified) "what is the chance that the second baby is a girl" period
Quote
A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?
I'd like to know how it simplified down to this because the original question states that one is a girl, it never specifies which one. It could be either one we don't know. Say for instance that we are given both girls. IF the clue was based on the first child GG so it is asking what the chance the other untested child is (non underlined). The underlined child is which child the "one" is referring to form the problem. (This makes it sound like it should be Neo from The Matrix, but I digress) Otherwise it is the exact reverse. If there is strictly one girl then it is an obvious which child the clue was based on. The clue can be generated from GG or GG or BG or GB. The first two are the same exact thing, so it does not effect the chance of outcome, it is just a different way of verifying the clue.


Quote
It's a simple given fact that the chance of ANY baby being born to be evenly split into boys or girls - and yes i had 2 years of mathematical chance calculus in highschool, as well as 6 years of biology (i was an A+ student at both) in which i learned about recessive & dominant genes and how to calculate those chances

I think most of us are quite intelligent, nerds and geeks tend to play old awesome games. And calculus has nothing to do with this, its statistics and probability :P. Respectfully, recessive and dominant genes have nothing to do with this problem, all that genes determine is the ratio that males are born vs females, which we agree on is slightly off from 50%, but it is close enough just to consider it equal. I am not quite sure why Sirbomber brought that up.

I'm kind of tired right now, so don't quote any of this until the morning as I probably will come back and edit it.
Title: A Women Has 2 Kids....
Post by: Eddy-B on August 09, 2009, 10:54:38 AM
Quote
Quote
the ORIGINAL question was (simplified) "what is the chance that the second baby is a girl" period
Quote
A women has 2 kids, and one of them is a girl. What is the chance that the other one is a girl?
I'd like to know how it simplified down to this because the original question states that one is a girl, it never specifies which one. It could be either one we don't know.
Regardless of which "one of them is a girl" .. you wanted to know the probability of the OTHER ONE. So if "the one girl" is the first born, than the question is about the second born. If "the one girl" is the second born, than you are asking about the first one. No matter how you look at your statement, you are asking about the other baby, in other words: the one baby that was not mentioned in the first part of your statement.


I will rephrase your question like this:
A woman has 20 kids. 19 of them are girls. What is the chance of the 20th kid to be a girl.


Answer: 50%  (give or take), and not 5%, which would be the answer if i follow your logic.

As mentioned before: the sex of all the other kids do NOT influence any next kid. The chance for a girl is still equal to the global average -wether that be 50% or 52%-



Can we close this thread?  this is getting pointless..
Title: A Women Has 2 Kids....
Post by: Hidiot on August 09, 2009, 11:03:48 AM
I swear I once heard on a Discovery channel someone saying that any second or later child has less and less chances of being a boy.

Since it doesn't interest me that much, I'll let someone else do the researching.
Title: A Women Has 2 Kids....
Post by: CK9 on August 09, 2009, 02:07:44 PM
If you don't cut out possible sibling relations, the chances change.
Title: A Women Has 2 Kids....
Post by: Kayedon on August 09, 2009, 03:11:35 PM
Ultimately, it falls upon how many apples or watermelons she ate.

(Sims 3 reference)
Title: A Women Has 2 Kids....
Post by: CK9 on August 09, 2009, 06:35:12 PM
of course, colony opinion is split between those who think the odds of having a girl are good, and those who are genetically manipulating those odds :P
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 09, 2009, 09:26:13 PM
Quote
of course, colony opinion is split between those who think the odds of having a girl are good, and those who are genetically manipulating those odds :P

Outpost Evening Star:
4/27/71 - A recent poll conducted by the Evening Star shows (not surprisingly) that colonist opinion is divided over the recent housing issues: 50% of all colonists responded that building more Residences was "important" or "extremely important" to them, while the other 50% of all colonists criticized the "pro-housers" for ignoring the recent food and oxygen shortages.  In a bold move, our fearless leader has submitted a proposal to handle both issues by limiting families to having only one child.  Couples who violate the new law will face strict punishment: one of the parents will be tossed out the nearest airlock as soon as the child is old enough to pick which parent s/he likes better.  Proponents of the new plan hail it as a shrewd plan necessary to preserve humanity, while critics condemn it as "a diabolical plan designed to encourage couples to have genetically-engineered children" which may result in a "gender imbalance" according to opposition leaders.  When asked to elaborate, Evening Star reporters received no response as a fist fight had apparently broken out between the two groups.  Reporters were forced to flee the area when the two sides broke into song and dance (http://www.youtube.com/watch?v=Uqxo1SKB0z8).  When interviewed, our fearless leader replied, "No comment."
Title: A Women Has 2 Kids....
Post by: speaker on August 09, 2009, 10:48:27 PM
when you said song and dance i immediately thought west side story fighting
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 10, 2009, 12:02:20 AM
Yes, that was the other option I considered.
Title: A Women Has 2 Kids....
Post by: CK9 on August 10, 2009, 12:28:08 AM
LOL!  Great one there bomber.  Is that (partially) an actual one from the game?
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 10, 2009, 08:41:38 AM
I tried to copy the style and use some common phrases ("our fearless leader"), but I wrote it off the top of my head.
Title: A Women Has 2 Kids....
Post by: CK9 on August 10, 2009, 04:04:48 PM
very nice
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 10, 2009, 10:06:21 PM
I'm glad you liked it.  Maybe I should do more of them?  But then they'd get stale.
Title: A Women Has 2 Kids....
Post by: Freeza-CII on August 10, 2009, 10:54:35 PM
Quote
"a diabolical plan designed to encourage couples to have genetically-engineered children" which may result in a "gender imbalance"

ok how is this going to imbalance things when the leader is making the choice of which one is which based on computation from the savant main frame. how ever the savant steered several convec at a cliff to make these computations.


This plan is more welcome then the last plan which was abortions till the correct gender was born. which again would get 100% results.
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 11, 2009, 06:35:40 PM
Quote
Regardless of which "one of them is a girl" .. you wanted to know the probability of the OTHER ONE. So if "the one girl" is the first born, than the question is about the second born. If "the one girl" is the second born, than you are asking about the first one. No matter how you look at your statement, you are asking about the other baby, in other words: the one baby that was not mentioned in the first part of your statement.

Ok I will write GB to show that the girl is born first and BG to show the boy is born first.

There are 3 outcomes GG, GB, BG. BB cannot occur.

Of those 3 how many are both girls? Only one. We had 3 to choose from so 1/3 is 33%.

Here is a crude method of looking at it. Assume statistics for births are 1:1, and for the sake of the example we have a perfect sample.

We ask 100 women who have exactly 2 kids what the sexes are. 25 say GG, 25 say GB, 25 say BG, and 25 say BB. We eliminate the BB group since it is an invalid data point. 25 are GG out of a remaining 75 moms.  This again leads to 1/3 or 33%.


To answer you question: 20 children 19 are girls, the chance of the unknown child being  a girl is: 4.761% (1/21) not 5%.
Title: A Women Has 2 Kids....
Post by: CK9 on August 12, 2009, 01:06:40 AM
that's assuming the order of birth matters.  If it does not, GB and BG are the same
Title: A Women Has 2 Kids....
Post by: Hooman on August 12, 2009, 10:30:33 PM
/sigh

People are just bringing up the same points again and again.

What Eddy-B seems to be saying, is that you phrased your question very poorly. I don't believe this is about what you meant. I believe it is about whether or not what you wrote actually means what you were thinking.


And yes, for the purpose of the meaning of the question, the order does matter.
 
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 13, 2009, 05:39:41 PM
I like how we've divided into two sides: The people who think we should be answering the "correct" question and the people who think we should answer the question that was actually asked.

The point is you should ask the question correctly the first time, then we won't get into debates about how we should answer the question.
Title: A Women Has 2 Kids....
Post by: Eddy-B on August 16, 2009, 08:31:52 AM
Dear Simpsonboy77,

I will assume your line of reasoning now:
As you have correctly stated, there are 4 possibilities: BB, BG, GB and GG.
Since you know one of them is already a girl, you can rule out the BB combination. You also have said it doesn't matter which one is the girl, which means BG and GB are in fact the same. So in the end you have 2 possibilities: GG and GB - or 50% chance for a girl, 50% chance for a boy.


As you can see, your reasoning is flawed, which is clearly illustrated by the second part of your reply (my 5% was just a simple rounded figure, and it should have been 1/21 = 4.7619047619047619047619047619048 %).  Anyway: your weird logic would say, the more girls are being born from the same mother, the less the chance becomes for the next one to be a girl.
With your logic; if a woman would've given birth to 99 girls, the chances for the 100th baby to be boy would be almost negligible?
I would even dare to say the opposite!!  If such a woman would exist, the chances of getting a boy, after 99 girls i would say are astronomical. Not from a mathematicle perspective, but from a biological one: her partner probably doesn't create Y-sperm to make boys....

Hopefully you would now agree that your "logic" doesn't make much sense when you look at it.


The bottom line is: the chance for a girl are just about the same as for a boy. No matter how you look at it.

---

Hooman:
If i would ask someone: "a woman has 2 children, what are the chances of both of them being a girl?"
== the answer would be 25%
If i changed the question to: "a woman has 2 children, 1 of which is a girl, what are the chances of both of them being a girl?"
== the answer is now 50% (and NOT 33% - no matter HOW you formulate the question!!). The reason is, very simply, because you can completely ignore the mentioned girl when it comes to the sex of the other one.

---

Sirbomber:
There may seem to be 2 "sides" of people here, but there really is only 1 answer to the question, unless you can re-formulate the question so that the answer becomes 33% (which i'm sure you can't).
Title: A Women Has 2 Kids....
Post by: Sirbomber on August 16, 2009, 10:35:10 AM
Quote
Sirbomber:
There may seem to be 2 "sides" of people here, but there really is only 1 answer to the question, unless you can re-formulate the question so that the answer becomes 33% (which i'm sure you can't).
That's what I was saying you fool.  I'm not saying there are two answers, I'm saying there are the people who have the right answer (you, me, CK9, etc) and the people who have the wrong answer/broken logic (Hooman/Simpsonboy99).
Title: A Women Has 2 Kids....
Post by: Hooman on August 16, 2009, 01:15:23 PM
Quote
Hooman:
If i would ask someone: "a woman has 2 children, what are the chances of both of them being a girl?"
== the answer would be 25%
If i changed the question to: "a woman has 2 children, 1 of which is a girl, what are the chances of both of them being a girl?"
== the answer is now 50% (and NOT 33% - no matter HOW you formulate the question!!). The reason is, very simply, because you can completely ignore the mentioned girl when it comes to the sex of the other one.

A woman has 2 children. What are the chances of both of them being a girl, given that at least one of them is a girl?

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You also have said it doesn't matter which one is the girl, which means BG and GB are in fact the same. So in the end you have 2 possibilities: GG and GB - or 50% chance for a girl, 50% chance for a boy.
This is false.

If the first kid is a girl, you can't have another kid and then suddenly call that first girl your second kid now. P(GB|G?) = 50%, P(BG|G?) = 0%. Saying that GB = BG for the sake of this question is nonsense.

This would appear to be the sticking point for the problem, based on what you've said.


The whole point of the ordering, is that you can't simply ignore the information about the kid that is given, as you don't know which kid it was.

What you're talking about is: A woman gives birth to a girl. What are the chances of a second birth also being a girl. This is not the qestion that was intended. It is also NOT the following question: A women has two kids, then one is chosen at random, and determined to be a girl, what is the probability that both kids are girls? The reason it is not this question either, is that the choice is not random. The only time the choice could have been made randomly, is if both kids were girls. In the other two cases, nature determines which one you're giving the information about.

The whole point is, both kids come first, the choosing comes second, and the choosing depends on the outcome of what the kids actually were. This is not a random choice.

 
Title: A Women Has 2 Kids....
Post by: Eddy-B on August 17, 2009, 01:16:16 AM
SirBomber: LOL :P
Hooman:
What you are saying is this:
the chances of any of the 4 possibilities is obviously 25%:
BB : 25%
BG : 25%
GB : 25%
GG : 25%
Everyone should be able to agree with me on this one (not taking into account the 52:48 ratio).
So going with this, there is a 25% chance for both kids to be a girl, correct?

Now, you are saying is that if you know the sex of one of them, the natural chance of the GG combination suddenly changes?? Chances don't change with new information about an existing situation. The chance for both of them being a girl is still 25%. It always will be, since there's a 50:50 ratio for sex.

Based on the question at hand "what is the chance of the OTHER one to be a girl", the question is about one specific event, NOT both births, and the answer is a simple 50:50 chance as it is for any child being born on this planet.

=====

Now, let's review the following situation:
Q1:  A woman gives birth to a girl. She gets pregnant again. What is the chance of this second baby to be a girl as well?  Is it 33%, or is it 50% ???   (i'll leave this question open for you to answer).

Q2: A woman gives birth to 2 children. The second baby was a girl. What is the chance of the first one being a girl?  Is it 33%, or is it 50% ???

=====

As i said before: new information does not chance an already calculated chance. Here's another example, in which i will provide new information, but in doing so, change the situation at hand (in which case the answer to the problem changes with it):

There's 100 randomly selected women, all of them have 2 children.
Chances are that 25 of them have 2 girls. Another 25 have 2 boys, and the rest (50) have a boy and a girl. This would illustrate my answer of 25%.
Now let's change the situation: let us select all the women that have at least one girl and discard the others: you are left with a DIFFERENT sample of only 75 women, since the other 25 have no girls.
This changes the answer to your 33%, although it is still the same 25 women we are talking about.

The essence here is that the sample has changed from 100 to 75, so the 2 answers cannot be compared with each other as they are from 2 totally different situations.



The question that simpsonboy asked is about 1 woman. The sample never changes, not even when i say one of the kids is a girl.

The simple fact remains that any person being born has a 50% chance of being female, no matter what the sex of his/her siblings is. Not even if he/she has 100 siblings (theoretically speaking).
Title: A Women Has 2 Kids....
Post by: Highlander on August 17, 2009, 12:09:51 PM
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Edit: Forgot to mention: the global average is 52F:48M because men tend to die younger than women.
Bleh, what a funny, but utterly useless topic in the end.

I'll add to the confusion I suppose.

The world average might be 52%/48% Female/Male. As Sirbomber said, this is due to Male's overall going around dying more than women. But in this question it is a matter of Birth Rates and not surviving population.

Nature does in fact "calculate" in the loss of Male's, so in terms of birthed children, I believe the % is 51.x% is born as males while 48.x% is born female.


Have fun :P
Title: A Women Has 2 Kids....
Post by: speaker on August 17, 2009, 02:58:11 PM
http://en.wikipedia.org/wiki/Hasty_generalization (http://en.wikipedia.org/wiki/Hasty_generalization)

the first and second child are independent, therefore regardless of whether the first child is a boy or a girl there is a 50:50% chance of the second being a boy or a girl.  Just like flipping a coin once and getting heads does not change the likelihood of getting a head on the second flip.
Title: A Women Has 2 Kids....
Post by: Simpsonboy77 on August 17, 2009, 06:58:53 PM
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SirBomber: LOL :P
Hooman:
What you are saying is this:
the chances of any of the 4 possibilities is obviously 25%:
BB : 25%
BG : 25%
GB : 25%
GG : 25%
Everyone should be able to agree with me on this one (not taking into account the 52:48 ratio).
So going with this, there is a 25% chance for both kids to be a girl, correct?

No need to keep restating something we all agree on, but yes true.

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Now, you are saying is that if you know the sex of one of them, the natural chance of the GG combination suddenly changes?? Chances don't change with new information about an existing situation. The chance for both of them being a girl is still 25%. It always will be, since there's a 50:50 ratio for sex.

Based on the question at hand "what is the chance of the OTHER one to be a girl", the question is about one specific event, NOT both births, and the answer is a simple 50:50 chance as it is for any child being born on this planet.

Ok with the chances we agreed on in the previous quote eliminate the BB one. GG is still 25%, but there is only a total of 75% of births that we should consider since 25% of them are BB and have been eliminated. Now do you see where your logic is flawed? You are taking into account something the question has stated as invalid.


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Now, let's review the following situation:
Q1:  A woman gives birth to a girl. She gets pregnant again. What is the chance of this second baby to be a girl as well?  Is it 33%, or is it 50% ???   (i'll leave this question open for you to answer).

Q2: A woman gives birth to 2 children. The second baby was a girl. What is the chance of the first one being a girl?  Is it 33%, or is it 50% ???
A1: 50%
A2. 50%

This proves nothing you eliminated a layer of uncertainty. In my question one of the two births is a girl, we have no information about one. You cannot break them up anymore. Your question is about 2 separate events.

Lets change your question slightly.
Q3 A woman gives birth to 2 children. The at least one of babies was a girl. What is the chance of the first one being a girl?  Is it 33%, or is it 50% ???

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There's 100 randomly selected women, all of them have 2 children.
Chances are that 25 of them have 2 girls. Another 25 have 2 boys, and the rest (50) have a boy and a girl. This would illustrate my answer of 25%.
You have a flawed selection, and are using that in your final answer.

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Now let's change the situation: let us select all the women that have at least one girl and discard the others: you are left with a DIFFERENT sample of only 75 women, since the other 25 have no girls.
This changes the answer to your 33%, although it is still the same 25 women we are talking about.

YES, YES THIS IS CORRECT!!!!!!

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The essence here is that the sample has changed from 100 to 75, so the 2 answers cannot be compared with each other as they are from 2 totally different situations.
They are not. You are reducing the general statistics to meet the

Look at it this way. From our 25:25:25:25 we know that we get one GG for every GB and BG. So if we combine them we get TWO girl/boy (order unspecific now) for every girl/girl.

75 women surveyed which means 50 have one girl one boy, and 25 have 2 girls because we must have a 2:1 ratio.

By your 50% logic if we interviewed 100 women who has 1 girl, then half of them will be GG, and 25% will be GB and 25% will be BG. How can this be if we established at the very top that GG, GB, and BG all had equal chances of occurring. You have changed the odds now.
Title: A Women Has 2 Kids....
Post by: Eddy-B on August 17, 2009, 10:43:48 PM
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http://en.wikipedia.org/wiki/Hasty_generalization (http://en.wikipedia.org/wiki/Hasty_generalization)

the first and second child are independent, therefore regardless of whether the first child is a boy or a girl there is a 50:50% chance of the second being a boy or a girl.  Just like flipping a coin once and getting heads does not change the likelihood of getting a head on the second flip.
My point exactly.
Title: A Women Has 2 Kids....
Post by: Hooman on August 17, 2009, 10:59:16 PM
Sounds to me like people are arguing from the same side of the fence. The question as first posted was badly phrased. That later part of Eddy-B's post is exactly what I took the question to mean after the answer was given. Before the answer was given, I also stated 50%. After the answer was given, I realized the question was poorly worded, and attempted to rephrase it to make the meaning he intended clear. A number of restastements were posted in this thread, and people seem to be arguing about two separate questions now.

In my last restatement:
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A woman has 2 children. What are the chances of both of them being a girl, given that at least one of them is a girl?
I meant precisely that woman was taken from a restricted sample space. Hence the "given" part with the extra info to restrict you to that sample space. The "a woman" part largely being used to mean we are choosing one person from that sample space.

But yes, the way you just stated it Eddy makes it much more clear.


This thread seems to have become more of a debate over English semantics than probability or statistics.


Simpsonboy, I have no idea what you said in your last paragraph, and I think you need to check that over.


Edit: Err, Eddy, did you just lock the thread?